Is there a difference between the two, or do they imply the exact same thing? If there is a difference, would you mind providing me with a definition of each please?

Well, I'd define that a "Computer" is what you and I are using right now to post this message.
But a "Computer System" or just "System" is everything this message board is made up of and how they help this message board to function.

For example, system consists of;
1. Computer(keyboard, monitor, CPU, etc: You and I need something to write a message)
2. Data (A Message itself)
3. Program (Message broad program, these are usually .exe file)
4. Server (Web server, Application server, Database server)
5. Some other applications (ICQ, emoticons, etc)
6. User (People posting a message)

I think 2-4 plays the most important roles. You need something to do a certain action. That will be the data. In this case, a message. The program does certain manipulations on the data. In this case that would be sending to the server, storing it there, and showing it later when someone wants to see it. The server is a where the program resides and the data is stored mainly.

I guess this is more of a system developer's view.

HH